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A298262
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Number of integer partitions of n using relatively prime non-divisors of n.
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1
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0, 0, 0, 0, 1, 0, 3, 1, 3, 2, 13, 1, 23, 7, 10, 8, 65, 5, 104, 11, 53, 53, 252, 8, 244, 124, 203, 67, 846, 22, 1237, 157, 636, 569, 1074, 51, 3659, 1140, 1827, 221, 7244, 236, 10086, 1162, 1844, 4169, 19195, 225, 17657, 2997
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OFFSET
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1,7
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LINKS
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FORMULA
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a(n) = Sum_{d|n} mu(n/d) * A098743(d).
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EXAMPLE
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The a(11) = 13 partitions: (65), (74), (83), (92), (443), (533), (542), (632), (722), (3332), (4322), (5222), (32222).
The a(14) = 7 partitions: (9 5), (11 3), (5 5 4), (6 5 3), (8 3 3), (4 4 3 3), (5 3 3 3).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], And[GCD@@#===1, !Or@@(Divisible[n, #]&/@#)]&]], {n, 50}]
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PROG
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b(n)={polcoef(1/prod(k=1, n, if(n%k, 1 - x^k, 1) + O(x*x^n)), n)}
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CROSSREFS
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Cf. A000041, A000837, A002577, A002865, A018818, A018819, A049820, A098743, A100953, A200745, A275870, A281116.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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